No president-elect in recent memory has so warmly and publicly embraced his party’s national chairman as Donald Trump hugged Republican National Committee Chairman Reince Priebus in the wee hours after Tuesday’s stunning election victory.

On Sunday Mr. Trump took his thanks a step further, making the RNC chairman the next chief of staff at the White House, along with tapping Stephen K. Bannon as his senior counselor and political strategist.

GOP insiders said it was a just reward for Mr. Priebus having successfully rebuilt the RNC after devastating presidential losses in 2008 and 2012 and guiding it safely past killer obstacles in the Republicans’ primary and nominating convention this time around.

The Wisconsin Republican managed to tame the presidential debate process, pull off a successful convention against strong internal opposition and build a turnout operation that some analysts have credited with helping Mr. Trump over the finish line Tuesday — all while shrugging off barbs from some Republicans who thought he mishandled Mr. Trump.

“I was surprised and encouraged to hear Trump give Reince credit for an unprecedented job preparing for the 2016 presidential election and for the subsequent success,” said Oregon GOP Chairman Bill Currier. “Many believe the RNC did not support Trump. I, however, saw nothing but equal support in the primary for all candidates and full support in the general for the nominee.”

The Trump transition team’s announcement was worded so as to set Mr. Priebus and Mr. Bannon up with equal ranking in the White House.

It means that when the chief of staff and the chief strategist are at odds, one doesn’t get to overrule the other — only the president will be able to do that.

Mr. Priebus will remain chairman until the RNC’s 168 members — three from each state and territory — elect a new chairman.

The as-yet-unset date for doing that now will have to be a week before the Jan. 20 swearing-in of Mr. Trump as president, because Mr. Priebus can’t legally hold both the chief of staff and national chairman jobs simultaneously.

The man Mr. Trump wants to succeed Mr. Priebus as RNC chairman is Corey Lewandowski, according to word making the rounds of the national committee. Mr. Lewandowski is thought to be a grass-roots type of conservative who is a personal friend and confident of the president-elect — and a bit scary to some in the GOP establishment. He was the first of three managers of Mr. Trump’s campaign.

Friends said Mr. Priebus, 44, wanted Mr. Trump to name him as White House chief of staff, considered one of the most powerful positions in the executive branch of government, since the holder of the job is the gatekeeper for the president, decides what documents he sees and has instant access to him 24/7.

The former Wisconsin GOP chairman wanted that more than an ambassadorship or a “K Street job” making serious money as a lobbyist or serving as the head honcho of a super PAC dedicated to uniting the conservative movement in the United States and those around the world.

The competition for chief of staff was hot. Mr. Bannon, the conservative media executive and sometimes-movie producer who took over the Trump campaign as CEO, might also have fit the bill. But his pick as political consigliere will scare the daylights out of many Republicans on Capitol Hill and of the establishment in general, Republican National Committee members agreed.

Still to be seen is what job will go to Kellyanne Conway, who was installed as campaign manager and helped stabilize the ship over the summer. She is now the only woman in American history to manage a successful presidential campaign, and relished the challenge.

When asked how she was qualified to manage a campaign, Ms. Conway told The Washington Times it would be hard to do worse than the political operatives who led the Republican Party to humiliating losses in the past two presidential elections. “I want my chance to fail as miserably as the Mitt Romney campaign failed,” she said.

But it’s Mr. Priebus who will have the gatekeeper’s job at the White House.

His pick drew rave reviews from some quarters of the conservative world. Pro-life leader Marjorie Dannenfelser, president of the Susan B. Anthony List, said naming Mr. Priebus was another important signal to pro-life voters that Mr. Trump understands them.

Tea party leaders, however, had signaled their displeasure ahead of the pick, saying Mr. Priebus was too much a figure of the Washington establishment.

Mr. Priebus is the only Republican to serve three conservative, two-year terms as the elected chairman of the national GOP’s governing body.

He took over in 2011 after defeating Michael Steele, the RNC chairman who served one term before him and left the committee broke, having alienated both major donors and many rank-and-file contributors.

Mr. Priebus faced criticism after 2012 nominee Mitt Romney lost what analysts said was a winnable election. President Obama and his turnout operation, the analysts said, outhustled the GOP.

The RNC’s autopsy report from that election rubbed some conservatives the wrong way by blaming the loss on the GOP’s reliance on consultants and on Mr. Romney’s hard-line stance on immigration. The report recommended the GOP instead embrace legalization.

The party’s conservative shock troops and its few commanders in Congress quickly sank that trial boat. The party would go on to nominate the strictest candidate on illegal immigration in major party history in Mr. Trump.